Improved Naive Bayes classifier with neural network models.
problem Limited complexity handling and independence assumption in Naive Bayes.
method Introducing Neural Naive Bayes and Neural Pooled Markov Chain models.
result Error rate reduced by 4.5 on IMDB dataset.
This paper tackles non-vacuous generalization bounds in ReLU networks by resolving rescaling invariances.
problem Non-vacuous generalization guarantees for ReLU networks with rescaling invariances.
method Proposes a lifted representation to resolve rescaling invariances and studies KL-based rescaling-invariant PAC-Bayes bounds.
result KL-based rescaling-invariant PAC-Bayes bounds provide tighter guarantees and resolve discrepancies in network complexity.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Graph neural networks extend neural Bayes estimators to irregular spatial data.
problem Estimating parameters from irregular spatial data with computational efficiency.
method Employing graph neural networks to approximate Bayes estimators for irregular spatial data.
result Extending neural Bayes estimation to irregular spatial data with computational benefits.
A new method estimates Bayes error for deep networks, suggesting they may have reached the limit.
problem Evaluating the performance of deep learning models and detecting overfitting.
method A simple and direct Bayes error estimator based on uncertainty of class assignments.
result Deep networks may have reached the Bayes error limit for benchmark datasets.
Study of Bayes optimal learning in high-dimensional linear regression with network side information.
problem Bayes optimal learning in high-dimensional linear regression with network side information.
method Introduce a Reg-Graph model and an iterative AMP algorithm for Bayes optimality under general conditions.
result Characterization of the limiting mutual information between latent signal and data observed.
Bayesian inference improves neural network pruning efficiency.
problem Reducing computational and memory demands of large neural networks.
method Utilizes Bayesian inference to calculate Bayes factors for iterative pruning.
result Achieves desired levels of sparsity while maintaining competitive accuracy.
PrAda-GAN improves synthetic data generation under differential privacy.
problem Generating synthetic data under differential privacy with marginal-based methods.
method Sequential generator architecture integrating GAN and marginal-based approaches, with adaptive regularization of Bayes network structure.
result PrAda-GAN outperforms existing methods in privacy-utility trade-off on synthetic and real-world datasets.
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
Post-hoc explanation methods are gaining popularity for interpreting, understanding, and debugging neural networks. Most analyses using such methods explain decisions in response to inputs drawn from the test set. However, the test set may have few examples that trigger some model behaviors, such as high-confidence fai…
Bayesian Empirical Bayes extends EB to complex structures using probabilistic symmetry.
problem Improving simultaneous inference in complex settings like arrays and graphs.
method Generalized empirical Bayes approach based on probabilistic symmetry.
result BEB outperforms existing methods in denoising arrays and spatial data.
Survey and compare PAC-Bayes bounds for bandit problems.
problem Designing and evaluating bandit algorithms with strong performance guarantees.
method PAC-Bayes bounds applied to bandit problems.
result PAC-Bayes bounds useful for offline bandit algorithms, but loose for online algorithms.
Neural Bayes methods simplify fitting complex bivariate extremal models.
problem Inference on complex multivariate extremal dependence models with computationally expensive likelihood functions.
method Use neural networks to approximate Bayes estimators and classifiers for model selection.
result Proposed neural Bayes methods enable routine implementation of complex extreme-value dependence models.
New clustering algorithm for time series data using RNN and variational Bayes.
problem Lack of generative model-based clustering methods for time series data.
method Recurrent Neural Network (RNN) with variational Bayes method.
result Robustness against phase shift, amplitude, and signal length variations.
Introduces PAC-Bayes bounds for understanding learning procedures.
problem Understanding the generalization ability of learning procedures.
method PAC-Bayesian bounds and their applications to neural networks.
result Simplified version of localization technique described.
Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.
problem Training two-layer ReLU networks using gradient descent in the mean field regime.
method Describes a condition for convergence to minimum Bayes risk, extending previous results to ReLU-activated networks.
result The condition for convergence does not depend on initialization and concerns weak convergence of network realization.
Bayes-optimal learning of a neural network with quadratic activations is achieved with GAMP-RIE.
problem Learning a neural network with quadratic activations from quadratic samples.
method Combining approximate message passing with rotationally invariant matrix denoising.
result Derives a closed-form expression for Bayes-optimal test error.
The paper improves risk certificate tightness for neural networks using PAC-Bayes bounds.
problem Improving the usability of risk certificates for neural networks based on PAC-Bayes bounds.
method Theoretical contributions including KL divergence bounds, efficient methodology for optimization, and methods for optimizing non-differentiable objectives.
result First non-vacuous generalization bounds on CIFAR-10 for neural networks.
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.
New complexity measure explains neural network generalization gap.
problem Understanding the generalization gap between neural networks and linear models.
method Introducing a new complexity measure for functions that governs PAC-Bayes bounds and relates to neural network complexity.
result Demonstrates a separation in sample complexity between 2 and 4-layer neural networks for periodic functions.
New work shows limits of certifying neural network robustness.
problem Certified training improves robustness but decreases accuracy.
method Bayes error analysis to investigate robustness limits.
result Upper bound for certified robust accuracy established.
In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the pr…
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert them into Ordered Decision Diagrams (ODDs), which are then used to reason about t…
New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
Efficient neural Bayes estimators for censored peaks-over-threshold models improve inference speed and accuracy.
problem Computational burden in inference with spatial extremal dependence models due to intractable or censored likelihoods.
method Developed neural Bayes estimators using data augmentation techniques to encode censoring information.
result Significant gains in computational and statistical efficiency compared to traditional methods.
In this draft, which reports on work in progress, we 1) adapt the information bottleneck functional by replacing the compression term by class-conditional compression, 2) relax this functional using a variational bound related to class-conditional disentanglement, 3) consider this functional as a training objective for…
In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN augmented Naive-Bayes and general BNs, where the latter two are learned using two variants of a conditional-independence (CI) based BN-learning algorithm. Experime…
We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second one derived from a novel PAC-Bayes bound. Both training objectives are evaluated o…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model uncertainty. Variational methods have been used for approximating intractable integrals t…
Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dime…
Evidence Networks simplify Bayesian model comparison for complex models.
problem Bayesian model comparison challenges with intractable likelihoods or priors.
method Loss functions and neural networks for fast, amortized estimation of Bayes factors.
result Evidence Networks provide accurate and scalable Bayes factor estimation.
Optimizes pruning masks for neural networks using probabilistic fine-tuning and PAC-Bayes bounds.
problem Improving neural network performance through adaptive pruning of weights.
method Optimizes stochastic pruning masks by minimizing expected loss, considering data-adaptive regularization and feature alignment.
result Probabilistic fine-tuning leads to improved test error over baseline methods in neural networks.
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally effic…
In this paper we present a new Bayesian network model for classification that combines the naive-Bayes (NB) classifier and the finite-mixture (FM) classifier. The resulting classifier aims at relaxing the strong assumptions on which the two component models are based, in an attempt to improve on their classification pe…
During the past five years the Bayesian deep learning community has developed increasingly accurate and efficient approximate inference procedures that allow for Bayesian inference in deep neural networks. However, despite this algorithmic progress and the promise of improved uncertainty quantification and sample effic…
The paper improves deep learning generalization bounds using PAC-Bayes compression.
problem Improving generalization bounds for deep neural networks.
method Quantizing neural network parameters in a linear subspace to develop tight generalization bounds.
result Large models can be compressed significantly, explaining Occam's razor.
Paper presents new training methods for neural networks with tighter risk certificates.
problem Training probabilistic neural networks with tighter risk certificates.
method Derived from PAC-Bayes bounds, two training objectives implemented for the first time in neural networks.
result Competitive test set errors and non-vacuous risk bounds with tighter values than previous results.
Proposes a new method for uncertainty estimation in neural networks.
problem Estimating uncertainty in neural networks.
method Samples outputs from Gaussian distributions parametrized by mean and variance sub-layers.
result Achieves better uncertainty quality than other methods.
Naive Bayes can be used as a discriminative classifier, matching the definition of logistic regression.
problem The definition of generative and discriminative classifiers.
method Comparing Naive Bayes and logistic regression, showing they can be used in either generative or discriminative ways.
result Naive Bayes can be used as a discriminative classifier.
Proposes a model combining graph networks and variational Bayes for graph data.
problem Probabilistic modeling of graph structured data.
method Combines graph networks and variational Bayes for probabilistic modeling of graph data.
result Demonstrates effectiveness on wind farm monitoring and Gaussian Process data.
Paper establishes statistical validity for variational Bayes in neural networks.
problem Lack of theoretical validity for Variational Bayes in Bayesian Neural Networks.
method Establishes posterior consistency for mean-field variational posterior in feed-forward neural networks.
result Proves VP concentrates around Hellinger neighborhoods of true density function under certain conditions.
Derandomizing PAC-Bayes bounds for smooth loss functions
problem Derandomizing PAC-Bayes bounds for smooth loss functions
method Exploiting smoothness properties of both the loss and the predictor class
result Bounds for deterministic predictors that involve flatness quantities
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
Study shows how classifiers can approach Bayes error in high-dimensional settings.
problem Generalization error in high-dimensional perceptrons.
method Proved a formula for generalization error using convex optimization and observed that logistic and hinge regression can approach Bayes error closely.
result Logistic and hinge regression can approach Bayes-optimal generalization error closely in high-dimensional settings.
New method improves training stochastic neural networks with tighter guarantees.
problem Training stochastic neural networks with provable guarantees.
method Developed partially-aggregated estimators and reformulated PAC-Bayesian bounds.
result Derives a differentiable objective leading to tighter generalisation guarantees.
Bayesian framework for policy learning in decision problems.
problem Maximizing expected welfare in decision-making problems.
method Loss-based Bayesian updating and squared-loss surrogate for welfare maximization.
result General Bayes posterior over decision rules with Gaussian pseudo-likelihood interpretation.
Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such as Bayes by Backprop or Multiplicative Normalising Flows). However, current appr…
LLEB uses a learned prior to quantify neural network uncertainty.
problem Quantifying uncertainty in neural network predictions.
method LLEB uses a learnable prior as a normalizing flow to maximize the evidence lower bound.
result LLEB performs on par with existing approaches in uncertainty quantification.